Torus (EntityTopic, 11)

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{{Shape|Torus|http://img56.imageshack.us/img56/5955/torus0oy.png|3|1, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]]Q|(21) ((x,y),z)|N/A|N/A|N/A|13}}
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{{Shape|Torus|http://img56.imageshack.us/img56/5955/torus0oy.png|3|1, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]]Q|(21) ((x,y),z)|N/A|N/A|N/A|13|N/A|N/A|pure}}
== Geometry ==
== Geometry ==
A '''torus''' is a special case of a [[surface of revolution]] where the base is a [[circle]]. The circle's radius is known as the '''minor radius''' and the distance from the center of the circle to the center of the torus is known as the '''major radius'''.
A '''torus''' is a special case of a [[surface of revolution]] where the base is a [[circle]]. The circle's radius is known as the '''minor radius''' and the distance from the center of the circle to the center of the torus is known as the '''major radius'''.

Revision as of 18:10, 18 June 2007

Template:Shape

Geometry

A torus is a special case of a surface of revolution where the base is a circle. The circle's radius is known as the minor radius and the distance from the center of the circle to the center of the torus is known as the major radius.

Equations

  • Assumption: Torus is centered at the origin, with the base in the xy plane.
  • Variables:
R ⇒ major radius of torus
r ⇒ minor radius of torus
  • All points (x, y, z) that lie on the surface of a torus will satisfy the following equation:
(R-sqrt(x2+y2))2 + z2 = r2
total edge length = 0
surface area = 4π2Rr
volume = 2π2Rr2
Unknown


Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind

Template:Rotope Nav